The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 5 cm longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line C) is 24 cm.
- Find the area of the shaded part.
- Find the perimeter of the dotted line. (Take π = 3.14)
(a)
Radius of the big semicircle above the dotted line
= 24 + 5
= 29 cm
Area of the big semicircle above the dotted line
= 3.14 x 29 x 29 x
12 = 1320.37 cm
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 24 x 24 x
12 = 904.32 cm
2 Shaded area above the dotted line
= 1320.37 - 904.32
= 416.05 cm
2 Radius of the small semicircle below the dotted line
= 24 - 5
= 19 cm
Area of the small semicircle below the dotted line
= 3.14 x 19 x 19 x 24
= 416.05 cm
2 Shaded area below the dotted line
= 904.32 - 416.05
= 488.27 cm
2 Total shaded area
= 416.05 + 488.27
= 904.32 cm
2 (b)
24 x 4 = 96 cm
Circumference of the curved lines
= 3.14 x 96
= 301.44 cm
Perimeter of the shaded area
= 301.44 + (5 x 2)
= 301.44 + 10
= 311.44 cm
Answer(s): (a) 904.32 cm
2; (b) 311.44 cm